Facebook has become massively popular and is still growing. While I am not particularly active on it, I recognize this is atypical. Think about how many devs ise FB OAuth for example, as it is insanely prolific.
Networks can fail at any time, but very few have after reaching escape velocity. Probably the most notable was AOL/IM and more recently the significant degradation of reddit. Networks must seriously mess up accross the 3 main identified categories, and not keep any pace with their users changing needs.
I would say the biggest threat to networks at scale, which oddly wasnt really discussed, is a failure to monetize or convert their network into value. Many people find twitter useful, for example, but it is rumored to be shopping itself around. If anything, the danger of networks is expecting data and adrevenue to be a sustainable business at scale. Obviously, it is a good problem to have 500million plus active users, but it is expensive and difficult. It is harder, one might inagine, to have 50m paying users.